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Express the induced emf as scalar triple...

Express the induced emf as scalar triple product of `vecv, vecB and vecl`.

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To express the induced electromotive force (emf) as a scalar triple product of the vectors \(\vec{v}\), \(\vec{B}\), and \(\vec{l}\), we can follow these steps: ### Step-by-Step Solution: 1. **Understanding Induced EMF**: The induced emf (\(E\)) in a circuit can be defined using the equation: \[ dV = -\vec{E} \cdot d\vec{r} \] ...
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veca.(vecbxxvecc) is called the scalar triple product of veca,vecb,vecc and is denoted by [veca vecb vecc]. If veca, vecb, vecc are cyclically permuted the vaslue of the scalar triple product remasin the same. In a scalar triple product, interchange of two vectors changes the sign of scalar triple product but not the magnitude. in scalar triple product the the position of the dot and cross can be interchanged privided the cyclic order of vectors is preserved. Also the scaslar triple product is ZERO if any two vectors are equal or parallel. (A) [vecb-vecc vecc-veca veca-vecb] (B) [veca vecb vecc] (C) 0 (D) none of these

veca.(vecbxxvecc) is called the scalar triple product of veca,vecb,vecc and is denoted by [veca vecb vecc] . If veca,vecb,vecc are coplanar then [veca+vecb vecb+vecc vecc+veca ] = (A) 1 (B) -1 (C) 0 (D) none of these

Let vecV = 2hati +hatj - hatk and vecW= hati + 3hatk . if vecU is a unit vector, then the maximum value of the scalar triple product [ vecU vecV vecW] is

If veca,vecb, vecc are unit coplanar vectors then the scalar triple product [2veca-vecb, 2vecb-c ,vec2c-veca] is equal to (A) 0 (B) 1 (C) -sqrt(3) (D) sqrt(3)

Why the induced emf is also called as back emf?

Let veca,vecb and vecc be three vectors. Then scalar triple product [veca vecb vecc] is equal to

Can scalar product be ever negative ?

Can scalar product be ever negative ?

Let vecb=-veci+4vecj+6veck, vecc=2veci-7vecj-10veck. If veca be a unit vector and the scalar triple product [veca vecb vecc] has the greatest value then veca is A. (1)/(sqrt(3))(hati+hatj+hatk) B. (1)/(sqrt(5))(sqrt(2)hati-hatj-sqrt(2)hatk) C. (1)/(3)(2hati+2hatj-hatk) D. (1)/(sqrt(59))(3hati-7hatj-hatk)

IF veca,vecb,vecc are three vectors such that each is inclined at an angle pi/3 with the other two and |veca|=1,|vecb|=2,|vecc|=3 then the scalar product of the vectors 2veca+3vecb-5vecc and 4veca-6vecb+10vecc is equal to

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